Shrinkwrap projection seems to ignore part of target mesh
Here is your topology:

It doesn't allow your object to bend and stick to the shape, an edge can't bend at its middle if there's no vertex. Instead, create this topology:

And it will work:

How to fill:

Delete the current topology and select the inner circle:



Extrude inwards with E:



Press CtrlR to create edge loops, press + to add more: